Lens polarization control

ABSTRACT

The invention is for a geodesic Luneberg lens antenna structure of nonplanar construction excited by horizontally and vertically polarized electromagnetic energy. Excitation of the lens by a single dual polarized feed will produce two divergent beams - one horizontally and the other vertically polarized. Excitation of the lens by two separate feeds at locations indicated by application of the criteria disclosed herein will result in the capability of providing arbitrary elliptical polarization including linear and circular polarization.

U4-1l -72 OR 396569165 D United States Patent [151 3,656,165 Walter et a1. [45] Apr. 11, 1972 [54] LENS POLARIZATION CONTROL 3,255,452 6/1966 Walter et al. ..343/753 [72] Inventors: Carlton H. Walter; Roger C. Rudduck; 3,255,454 6/1966 Walter et a1. ..343/91 1 X 82*," Ryan, of Columbus, FOREIGN PATENTS OR APPLICATIONS 876,304 8 1961 'B 't ..34 54 [73] Assignee: The Ohio State University Research Foun- Great n am 3/7 damn Columbus Ohm Primary Examiner-Paul L. Gensler [22] Filed: Sept. 18, 1968 Attorney-Anthony D. Cennamo Related Applicamm Data The invention is for a geodesic Luneberg lens antenna struc- [63] Continuatiomimpan of 431 890 Feb H ture of nonplanar construction excited by horizontally and 965 abandone vertically polarized electromagnetic energy. Excitation of the lens by a single dual polarized feed will produce two divergent 52 us. Cl .543/754, 343/756, 343/761, beams one horizontally and the other vertically Polarized 343/91 L Excitation of the lens by two separate feeds at locations in- 51 lnt.Cl. ..H0lq19/06 dieated y application of the criteria disclosed herein will [58] Field of Search ..343/753, 754, 911, 911 L result in the Capability of providing arbitrary elliptical polarization including linear and circular polarization. 56 R f C't d I 1 e erences l e 6 Claims, 9 Drawing Figures UNITED STATES PATENTS 2,814,040 11/1957 Warren ..343/ 3 X BEAM DIRECTION e=9o--, 5 (TI-: M0087: B

OR E9 (T5 MoDEi R ADIAL LINE OF FEED 54 CONICAL PORTION OF LENS so WAVEGUIDE FEED AT POSITION (r M CONTOURED PORTION OF FEED POSITION 58 LENS PATENTEDAPRH I912 656.16

SHEET 1 [1F 4 Lens Axis Typical Roy Path LEN S CONTOURED SECTION CONICAL K =0 SURFACE sgcnou Mean Surface F Aluminum "Flops" INVENTORS,

CARLTON H. WALTER, ROGER C. RUDDUCK 4 CHARLES E. RYANJR.

PATENTEDAPR 11 I972 3,656,165

SHEET 2 BF 4 ELEVATION AXI F ANGLE y SYhfiMETRY ARBITRARY POLARIZATION 0.84 TE MODE y WAVEGUIDE LENS 0.14 FEED APERTURE GROUND PLANE LOCATIONS LENS TEM MODE WAVEGUIDE FEED FIG. 2

e(TEM mode) I E ,,MDDE) AXIS OF SYMMETRY ORTHOGONAL FEED Q82 PROBES LENS CROSS SECTION IN PLANE/ AT WAVEGUIDE FEED \DUAL MODE WAVEGUIDE FEED IN VIL'N'U )RS CARLTON H.WALTER ROGER C. RUDDUCK HY CHARLES E. RYAN,JR.

ATTORNEY PATENTEDMR 1 1 m2 SHEET 3 [IF 4 INVENTORS CARLTON H- WAL TE R,

ROGER C. RUDDUCK, CHARLES E. RYAN, JR.

ATTOMFY PATENTEDAPRH I972 3.656.165

. SHEET u 0F 4 K o o OI C: BEAM DIRECTION (-6- 90 B, (b (hp-I80) W 0 (TE MODE RADIAL LINE OF FEED CONICAL PORTION OF LENS so WAVEGUIDE FEED AT POSITION (r D 56 I CONTOURED PORTION OF FEED POSITION 58 LENS F l G. 5

Z FEED DETAIL WAV U MEAN SURFACE EG wAvEeumE FLANGE (CONNECT TO SOURCE OR RECEIVER) TE MoDE 0R TEM MODE INVENTOR. CARLTON ll. HLTER ROGER C. RUDDUCK CHARLES E. RYANJR.

LENS POLARIZATION CONTROL This application is a continuation-in-part of Ser. No. 431,890, filed Feb. 11, 1965, now abandoned.

BACKGROUND In the patent issued to C. H. Walter, No. 3,108,278, for Surface Wave Luneberg Lens Antenna System, there is disclosed a surface wave structure that can be made to perform as a Luneberg lens. In particular, it was shown that the index of refraction of a surface wave structure can be made to conform to the equation:

' Eq. 1. (c/v)=n= /2T, where c= velocity of light in free space v phase velocity of the surface wave r= normalized radius.

It is further shown that a circular dielectric sheet on a ground plane can be made to perform as a Luneberg lens in the plane of the sheet and at the same time perform as an endfire antenna in the orthogonal plane.

In the patent issued to C. H. Walter and R. C. Rudduck, No. 3,255,454, for Surface Wave Luneberg Lens Antenna System, there is disclosed a surface wave structure operable as a Luneberg lens although its contour may be other than planar. This antenna adapts the teachings of the prior patent to more practical applications. That is, the nonplanar surface wave structure may be fitted flush with the skin of the aircraft, vehicle or craft upon which the antenna is to be mounted.

SUMMARY The lenses disclosed therein have the capability of radiating a beam at an arbitrary angle with respect to the plane of the lens rim. These previously disclosed geodesic lens models have employed the TEM waveguide mode which has a frequency-independent index of refraction, thus providing wide bandwidth for vertical polarization. Horizontal polarization is achieved by the use of the TE waveguide mode, but the index is frequency-dependent.

Theoretical considerations of beam elevation positioning, the frequency dependence of the phase velocity, and the polarization properties of the TE mode suggest that a lens utilizing the TE. waveguide mode may be utilized to obtain horizontal polarization. Accordingly, a lens of thesame design as the TEM mode beam elevation positioning lens but utilizing the TE waveguide mode has been constructed and tested. It was found that the lens will position either a horizontally polarized or a vertically polarized beam over a range of elevation angles. Since a TE lens will also support the TEM mode, vertical polarization can be obtained from the same lens. It was further found, however, that for the same feed radius the respective beam elevation angles for the two polarizations do not coincide. Thus a single dual polarized feed may be used to obtain two beams'(one vertically polarized, the other horizontally polarized) at the same azimuth angle but having different elevation angles. Alternatively, through the use of beam elevation positioning of two feeds situated on the same radial line, one operating in the TEM mode and the other operating in the TE mode, arbitrary polarization of a single beam can be achieved.

OBJECTS It is accordingly the primary object of the present invention to provide a new and improved geodesic Luneberg lens antenna having both horizontal and vertical polarization capabilities.

It is a further object of the present invention to provide a new and improved geodesic Luneberg lens antenna having horizontal and vertical polarization in a single beam.

It is another object of the present invention to provide a new and improved geodesic Luneberg lens antenna utilizing a TE waveguide mode to achieve horizontal polarization.

Further objects and features of the present invention will become apparent from the following detailed description when taken in conjunction with the drawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I and la are schematic illustrations of a nonplanar lens;

FIG. 2 is a cross-sectional illustration of a lens of the present invention illustrating dual polarization in a single beam;

FIG. 2a is a cross-sectional illustration of a lens of the present invention illustrating dual polarization in separate beams;

FIG. 3 is a cross-sectional illustration of a lens of the present invention illustrating the TE mode of beam elevation positionmg;

FIG. 3a is a cross-sectional illustration of a lens of the present invention illustrating the physical structure of the lens and the physical connection of the feed means to the lens; and,

FIG. 4 is a schematic illustration of a flared waveguide feed utilized in the present invention.

FIG. 5 is an isometric pictorial view of an actual constructed embodiment of the invention;

FIG. 6 is a sectional view showing the waveguide feed of the embodiment of FIG. 5.

DETAILED DESCRIPTION OF THE DRAWINGS Referring now to FIG. 1 there is given an analysis of the radiation characteristic of the Luneberg lens as set forth in the aforementioned patents. FIGS. 1 and 1a are schematic diagrams of the coordinate systems used in the analysis of the instant invention. It was shown that the law for a ray in a circularly symmetric lens is Eq. 2. n(r) rsin= K where n(r) is the index of refraction at radius r,

K is the constant for each ray,

r is the radius in cylindrical coordinates,

4: is the angle between the ray path and the meridian on the lens surface.

For a lens required to radiate at the angle B from the plane of the lens rim, the combination of index of refraction and contour must be chosenso that the relationship between the ray constant K and the exit angle 0,, satisfies the expression,

Eq. 3. K=sin 0,, cost? where 0,, is as shown in FIG. la.

Another expression which describes the ray paths in a circularly symmetric lens and which is equivalent to Eq.2.is given by where z= dz/dr is the slope of the lens contour.

The index of refraction for a wave propagating in a TE mode in a parallel plate lens is a function of the plate spacing d, the constitutive parameters u, E of the media and the free space wavelength given by Eq. 5. n #1., e,-- (X5723) 2 where A, is the free-space wavelength. For an air-filled geodesic lens, 1., e, I. In order that higher-order modes other than the TE mode do not propagate, it is necessary that d ll geometries are maintained in the lens. However, the value of K for a given ray path is also changed by the same factor. These properties are evident from Eq. 4 which describes the ray path geometries. Thus using Eqs. 2 and 3 to relate differing indices of refraction to their corresponding beam elevation angles, we have To? cos B. T

This result indicates that the effect of a constant multiplier (N) of the index of refraction is a displacement of the beam in elevation.

It follows from Eq. 5 that a constant-index geodesic lens with uniform plate spacing and uniform dielectric throughout the lens will be a constant-index lens at any frequency above cut off. If the lens contour is properly designed for lens action at angle B, for frequency f then lens action will be obtained at angle [3 for frequency f as determined from Eqs. 5 and 7. Since the index of refraction is a function of frequency as given by Eq. 5, the beam elevation angle may be frequency scanned. In particular, a unit-index geodesic lens of constant plate spacing when operated in the TE mode will radiate a horizontally polarized beam at an elevation angle given by Eq. 8. C056 P y/ 1 (h /2d 2 cos B where B is the TEM mode beam angle. Equation 8 also indicates that the previous results concerning beam elevation positioning may be applied to the TE mode geodesic lens. In this method the beam elevation angle is controlled by radial feed position. Thus Eqs. 5 and 8 allow one to adapt a successful TEM mode geodesic lens for simultaneous operation of the TE mode. As previously mentioned, this provides the capability of arbitrary polarization in a single beam, or, dual polarization in a single beam (see FIG. 2), or dual polarization in separate beams (see FIG. 2a). FIGS. 2 and 2a illustrate these properties.

In the last aforementioned patent, the ,8 40, r 0.82 lens was experimentally investigated because of its low deterioration in focusing over a wide range of beam elevation angles. In the TEM mode, this lens design will basically give beam positioning over the range B 90. Values of beam elevation angles for the TE mode at various feed radii, computed from previous results through the use of Eq. (7), have been determined. These results apply to the unit-index, B 40, r 0.82 lens design and are valid for the TE mode with a plate spacing of 1.06 )t Perfect focusing for a given value of feed radius r occurs when the values of B" are the same for all values of K, this occurs when r r 0.82. For all other values of feed radius the values of [3" over a range of K values are not identical. However, if the values of ,8" do not differ greatly, the beam will focus approximately over a wide range of elevation angles. This properly has been verified by measurements.

Beam elevation positioning can be used to compensate for the natural frequency steering of the TE lens as expressed by Eq. 8. For example, a horizontally polarized beam may be stabilized in elevation over a frequency range by a compensating radial movement of the feed. Another alternative would be the use of a long feed structure designed so that its phase center tracks in frequency along the lens radius to give vertical beam stabilization.

It is also noted that the multiplier N as given by Eq. 7 does not affect the focusing properties of the lens. Thus the lens has as good focusing properties for the TE mode as for the TEM mode but with the beam elevation position as given by Eq. 8. From a specific feed position, the radiated beam will have an elevation angle ranging from broadside to the plane of the lens rim at waveguide cutoff frequency to an asymptotic approach to the TEM beam elevation angle with increase in frequency. At low frequencies of operation, the obtainable elevation coverage decreases because the value of B" for each feed position increases with decrease in frequency. This property determines the lower frequency limit on bandwidth and depends on the vertical coverage required. The upper frequency limit is determined by higher-order mode excitation and conversion. Bandwidth limitations may also depend on other factors, e.g., element pattern of the aperture.

Based on theoretical considerations described in the previous sections and the performance of a parallel-plate geodesic lens, TEM mode lens, a TE. lens of the [3 40, r 0.82 contour was constructed and tested having the parameters of FIG. 3. The tolerances on plate spacing for a T15 lens are much more stringent than those for a TEM lens because the index is independent of plate spacing for the latter. In addition, for X- band operation, it was necessary to increase the spacing d between plates 10 and 12 from the value of /5 inch used in the TEM mode lens. A plate spacing of 1 Va inches was chosen for the TE mode lens. Stiffening rings 14 and 16 of 5/8 inch diameter were placed on either end. A distance of 9.75" from the center line 20 to either end 22 or 24 defined the diameter. An angle of 47.74 for the slope of sides 26 and 28 and an angle of 67.5 defined the contour of the particular geodesic lens used to test the dual polarization properties described above.

It is noted that the aperture width of the TE lens is greater by a factor of 2.25 than the aperture of the TEM mode beam elevation positioning lens of the last named patent. This fact results in the aperture element pattern of the TE lens being more directive than the aperture element pattern of the TEM lens, and thus tends to cause a greater fluctuation in gain as the beam is steered than would occur for smaller plate spacing. The physical structure of the lens including the feed means is illustrated in FIG. 3a.

The E-field patterns of the TE lens fed by a butted waveguide of FIG. 4 exciting the lens in a TE mode were taken for several radial feed positions (denoted by r at a frequency of 10 Gc. The E-field patterns of the TE lens fed by a butted flap waveguide of FIG. 4 exciting the TEM mode were also taken for the same feed positions. Again the patterns were taken at a frequency of 10 Gc.

The feed for these measurements (flap waveguide) is shown in structural detail in FIG. 4. The flaps 30 and 32 are provided to avoid excessive illumination of the rear portion of the aperture 34 and to effect efficient coupling of energy into the feed 36.

Values of gain corresponding to the measurements taken are given in the Table appended hereto. In addition to the gain measurements, extensive pattern measurements were taken for r 0.766 and the directivity was computed. The resulting value of directivity was 28.7 db, while the measured gain was 2 l .6 i 0.3 db.

The lens is seen to exhibit beam elevation angle positioning properties for both polarizations, as predicted by theory. The directivity deterioration of the beam and consequent loss of gain for angles near the plane of the lens may be largely attributed to the element pattern directivity of the lens aperture. Deterioration of the beam at angles near the normal to the lens may be attributed to both element pattern directivity and cancellation due to polarization. Thus while the larger aperture gives greater directivity in a preferred direction, it tends to limit the scanning ability of the lens. In order to attain a more nearly constant directivity over the scanning region, it is preferred to decrease the aperture of a TEM mode lens although reducing directivity in a preferred direction. In a TE mode lens, the aperture size is dictated by Eqs. 5 and 6, which give the plate spacing necessary to maintain a TIE mode. It is seen that by loading the lens with dielectric, the aperture size may be reduced. Since dielectric material usually increases losses and lower power-handling capability, the amount of dielectric might be reduced by tapering the plate spacing so that loading is required only near the lens rim. Account must also be taken of the effect of dielectric loading on the TEM mode performance for a dual polarized lens.

Since the lens will support both the TEM and TE modes, which for a single feed at a given feed radius radiate at different elevation angles, it is possible to use both polarizations simultaneously at the same azimuth angle (but at different elevation angles) by using a dual-polarized feed such as a square waveguide with orthogonal coupling probes, as shown in FIG. 20. Alternatively, either polarization may be used at given azimuth and elevation angles by using appropriate separate feeds. In this way multiple beams of either polarization may be obtained over a range of azimuth and elevation angles.

In order to obtain arbitrary polarization at a specific azimuth angle and elevation angle, it is necessary to use linearly polarized feeds located on the same radial line but at different feed radii governed by the beam elevation angles for the two polarizations as shown in FIG. 2. In this way the angles of the beam maxima for both polarizations can be made to coincide, allowing arbitrary polarization to be obtained by adjusting the amplitude and phase of the feeds. The azimuth angle ofthe radiated beam is diametrically opposite the feed location. Thus, the TEM and TE modes provide the space quadrature of the E-field components, while the phase between the two feeds provides the time quadrature between the E-field components which is required for circular polarization. Adjustment of the amplitude excitation of the feeds then allows any elliptical polarization state to be attained. By using a feed arrangement of this type, circular polarization could be obtained.

Thus the developments discussed above allow the extension of successful TEM mode geodesic lens designs to TE mode operation or to simultaneous TEM and TE mode operation. This results in a geodesic lens antenna having arbitrary polarization capability including dual polarization, circular polarization, and polarization diversity.

In order to illustrate in actual practice the principles of the heretofore schematic embodiments of the antenna of the present invention, reference is made to FIGS. 5 and 6 illustrating pictorially the actual constructed embodiment of the present invention. In order to more fully appreciate the embodiments shown in FIGS. 5 and 6, the sectional components of the antenna are included therein together with the XYZ axes and the angle of the radiated beam. More specifically, the lens 50 positioned in the ground plane 48, has a circular lens aperture 52, a conical portion 54 and a contoured portion 56. At the feed position 58 there is positioned the waveguide feed 60. The waveguide feed 60 is shown more specifically in the cross sectional view of FIG. 6.

Accurate to I 03 db.

What is claimed is:

l. A frequency-scanned dual polarization beam positioning antenna structure comprising a nonplanar parallel plate geodesic Luneberg type lens including two parallel plates each formed by a surface of revolution, means to couple horizontally and vertically polarized electromagnetic energy to said lens to provide said lens with the capability of radiating beams at angles, [3 from 0 to with respect to the plane of the rim of said lens; said lens providing the propagation of a horizontally polarized beam by controlling the index of refraction between said parallel platss by satisfying the relation n where 11., is the permeabilit y o f thmedia, e, is the permittivity of the media, A, is the free-space wavelength and d is the spacing between said parallel plates; said horizontally polarized beam radiating at an elevation angle related to the elevation angle of a vertically polarized beam when said index of refraction is unity in accordance with the an ular relation cos B V l (A 722) 2 cos fl p where B is said horizontally polarized beam elevation angle and By is said vertically polarized beam elevation angle.

2. A frequency-scanned dual polarization beam positioning antenna structure as set forth in claim 1 wherein said means to couple electromagnetic energy to said lens comprises a single dual polarized feed to excite said lens with horizontally and vertically polarized electromagnetic energy at a single feed radius, said lens radiating horizontally and vertically polarized beams on the same azimuth line but at different elevation angles in accordance with said angular relationship.

3. A frequency-scanned dual polarization beam positioning antenna structure as set forth in claim 2 wherein said single feed further comprises a square waveguide feed with orthogonal excitation probes. J

4. A frequency-scanned dual polarization beam positioning antenna structure as set forth in claim 1 wherein said means to couple electromagnetic energy to said lens comprises two electromagnetic feeds, the first of said feeds providing horizontal polarization and the second of said feeds providing vertical polarization, said feeds located on the same radial line with different feed radius that satisfy said angular relationship to permit said angle [3, to equal said angle B 5. A frequency-scanned dual polarization beam positioning antenna structure as set forth in claim 4 wherein said means to couple electromagnetic energy to said lens further comprises means to provide arbitrary elliptical polarization including linear and circular polarization, said means further including means to control the amplitude and phase of said horizontal and vertical polarization.

6. A frequency-scanned dual polarization beam positioning antenna structure comprising a nonplanar parallel plate geodesic Luneberg lens including two parallel plates each formed by a surface of revolution, a ground plane structure integrally formed with the surface of said lens with radial symmetry propagation capability, means to couple horizontally and vertically polarized electromagnetic energy to said lens to provide said lens with the capability of radiating beams at angles, ,8, from 0 to 90 with respect to the plane of the rim of said lens; said lens providing the propagation of a horizontally polarized beam by controlling the index of refraction between said parallel plates by satisfying the relation 71 #4 r 2 where u, is the permeability of the media, 6, is the permittivity of the media, A, is the freespace wavelength and d is the spacing between said parallel plates; said horizontally polarized beam radiating at an elevation angle related to the elevation angle of a vertically polarized beam when said index of refraction is unity in accordance with the angular relation cos e l (A /2d) cos 1, where [3, is said horizontally polarized beam elevation angle and [3, is said vertically polarized beam elevation angle. 

1. A frequency-scanned dual polarization beam positioning antenna structure comprising a nonplanar parallel plate geodesic Luneberg type lens including two parallel plates each formed by a surface of revolution, means to couple horizontally and vertically polarized electromagnetic energy to said lens to provide said lens with the capability of radiating beams at angles, Beta , from 0* to 90* with respect to the plane of the rim of said lens; said lens providing the propagation of a horizontally polarized beam by controlling the index of refraction between said parallel plates by satisfying the relation n square root Mu r Epsilon r - ( lambda 0/2d) 2 where Mu r is the permeability of the media, Epsilon r is the permittivity of the media, lambda o is the free-space wavelength and d is the spacing between said parallel plates; said horizontally polarized beam radiating at an elevation angle related to the elevation angle of a vertically polarized beam when said index of refraction is unity in accordance with the angular relation cos Beta HP square root 1 - ( lambda o/2d) 2 cos Beta VP where Beta HP is said horizontally polarized beam elevation angle and Beta VP is said vertically polarized beam elevation angle.
 2. A frequency-scanned dual polarization beam positioning antenna structure as set forth in claim 1 wherein said means to couple electromagnetic energy to said lens comprises a single dual polarized feed to excite said lens with horizontally and vertically polarized electromagnetic energy at a single feed radius, said lens radiating horizontally and vertically polarized beams on the same azimuth line but at different elevation angles in accordance with said angular relationship.
 3. A frequency-scanned dual polarization beam positioning antenna structure as set forth in claim 2 wherein said single feed further comprises a square waveguide feed with orthogonal excitation probes.
 4. A frequency-scanned dual polarization beam positioning antenna structure as set forth in claim 1 wherein said means to couple electromagnetic energy to said lens comprises two electromagnetic feeds, the first of said feeds providing horizontal polarization and the second of said feeds providing vertical polarization, said feeds located on the same radial line with different feed radius that satisfy said angular relationship to permit said angle Beta HP to equal said angle Beta VP.
 5. A frequency-scanned dual polarization beam positioning antenna structure as set forth in claim 4 wherein said means to couple electromagnetic energy to said leNs further comprises means to provide arbitrary elliptical polarization including linear and circular polarization, said means further including means to control the amplitude and phase of said horizontal and vertical polarization.
 6. A frequency-scanned dual polarization beam positioning antenna structure comprising a nonplanar parallel plate geodesic Luneberg lens including two parallel plates each formed by a surface of revolution, a ground plane structure integrally formed with the surface of said lens with radial symmetry propagation capability, means to couple horizontally and vertically polarized electromagnetic energy to said lens to provide said lens with the capability of radiating beams at angles, Beta , from 0* to 90* with respect to the plane of the rim of said lens; said lens providing the propagation of a horizontally polarized beam by controlling the index of refraction between said parallel plates by satisfying the relation n Square Root Mu r epsilon r - ( lambda o/2d) 2 where Mu r is the permeability of the media, epsilon r is the permittivity of the media, lambda o is the free-space wavelength and d is the spacing between said parallel plates; said horizontally polarized beam radiating at an elevation angle related to the elevation angle of a vertically polarized beam when said index of refraction is unity in accordance with the angular relation cos epsilon HP Square Root 1 - ( lambda o/2d)2 cos lambda VP where Beta HP is said horizontally polarized beam elevation angle and Beta VP is said vertically polarized beam elevation angle. 